CORE_MATH • SHS 1Term 2WAEC / WASSCE SyllabusVIP Lesson
Variation (Direct, Inverse, Joint & Partial)
Constant of proportionality, modeling direct, inverse, joint, and partial variation, and solving real-world word problems.
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Real-World Context & Relevance in Ghana
Electricity tariffs in Ghana often involve partial variation: a fixed monthly standing charge plus a variable charge proportional to kilowatt-hours consumed.
Key Syllabus Learning Objectives
- 1Formulate mathematical equations from direct, inverse, and joint variation statements
- 2Calculate the constant of proportionality k from given boundary values
- 3Set up and solve simultaneous equations for partial variation problems
- 4Determine percentage changes in dependent variables when independent variables change
1
Partial Variation and Simultaneous Equations
In partial variation, the formula has two parts: y = a + bx. Candidates are given two pairs of values for (x, y), which produce two simultaneous equations to solve for constants a and b.
- Write: y = c + kx.
- Substitute (x₁, y₁) to get Equation (1).
- Substitute (x₂, y₂) to get Equation (2).
- Eliminate c by subtraction to find k, then find c.
Core Takeaway:
Partial variation always yields two simultaneous linear equations.
WAEC / WASSCE Examiner Tips
- Always state the constant of proportionality clearly (e.g. "where k is a constant").
- State the formula connecting the variables as a standalone answer before calculating further values.
- In inverse variation, remember that if x doubles, y is halved.
Common Candidate Pitfalls & Errors to Avoid
- Writing direct variation as y = k/x or inverse variation as y = kx.
- In partial variation, omitting the constant term and treating it as direct variation.
- Failing to square or cube terms when a problem says "varies inversely as the square of x".
Topic Mastery Checklist
- Can I set up y = k/x² for an inverse-square variation?
- Can I solve a partial variation problem y = a + bx?
- Can I find the percentage change in y when x increases by 20%?
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